{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multipath Fading\n",
    "\n",
    "In this chapter we introduce multipath, a propagation phenomenon that results in signals reaching the receiver by two or more paths, which we experience in real-world wireless systems. So far we have only discussed the “AWGN Channel”, i.e., a model for a wireless channel where the signal is simply added to noise, which really only applies to signals over a cable and some satellite communications systems."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating Rayleigh Fading\n",
    "\n",
    "Rayleigh fading is used to model fading over time, when there is no significant LOS path. When there is a dominant LOS path, the Rician fading model becomes more suitable, but we will be focusing on Rayleigh. Note that Rayleigh and Rician models do not include the primarily path loss between the transmitter and receiver (such as the path loss calculated as part of a link budget), or any shadowing caused by large objects. Their role is to model the multipath fading that occurs over time, as a result of movement and scatterers in the environment.\n",
    "\n",
    "There is a lot of theory that comes out of the Rayleigh fading model, such as expressions for level crossing rate and average fade duration. But the Rayleigh fading model doesn’t directly tell us how to actually simulate a channel using the model. To generate Rayleigh fading in simulation we have to use one of many published methods, and in the following Python example we will be using Clarke’s “sum-of-sinusoids” method.\n",
    "\n",
    "To generate a Rayleigh fading channel in Python we need to first specify the max Doppler shift, in Hz, which is based on how fast the transmitter and/or receiver is moving, denoted \\Delta v. When the velocity is small compared to the speed of light, which will always be the case in wireless communications, the Doppler shift can be calculated as:\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Alt text](<Screenshot 2024-01-12 151124.png>)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We also choose how many sinusoids to simulate, and there’s no right answer because it’s based on the number of scatterers in the environment, which we never actually know. As part of the calculations we assume the phase of the received signal from each path is uniformly random between 0 and 2\\pi. The following code simulates a Rayleigh fading channel using Clarke’s method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Doppler shift: 17.881555555555558\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Simulation param\n",
    "v_mph = 60  # velocity of RT/TX\n",
    "Fc = 200e6  # RF carrier freq (center freq)\n",
    "Fs = 1e5    # Sample rate of simulation\n",
    "N = 100     # Num of sinusiods to sum\n",
    "\n",
    "v = v_mph*(1609.34)*(1/60)*(1/60) # Convert to m/s\n",
    "fd = v*Fc/3e8\n",
    "print(\"Max Doppler shift: \"+str(fd))\n",
    "t = np.arange(0, 1, 1/Fs) # time vector. (start, stop, step)\n",
    "x = np.zeros(len(t))\n",
    "y = np.zeros(len(t))\n",
    "\n",
    "for i in range(N):\n",
    "    alpha = (np.random.rand() - 0.5) * 2 * np.pi\n",
    "    phi = (np.random.rand() - 0.5) * 2 * np.pi\n",
    "    x = x + np.random.randn() * np.cos(2 * np.pi * fd * t * np.cos(alpha) + phi)\n",
    "    y = y + np.random.randn() * np.sin(2 * np.pi * fd * t * np.cos(alpha) + phi)\n",
    "\n",
    "# z is the complex coefficient representing channel, you can think of this as a phase shift and magnitude scale\n",
    "z = (1/np.sqrt(N)) * (x + 1j*y) # this is what you would actually use when simulating the channel\n",
    "z_mag = np.abs(z) # take magnitude for the sake of plotting\n",
    "z_mag_dB = 10*np.log10(z_mag) # convert to dB\n",
    "\n",
    "# Plot fading over time\n",
    "plt.plot(t, z_mag_dB)\n",
    "plt.plot([0, 1], [0, 0], ':r') # 0 dB\n",
    "plt.legend(['Rayleigh Fading', 'No Fading'])\n",
    "plt.axis([0, 1, -15, 5])\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mitigating Multipath Fading¶\n",
    "\n",
    "## CDMA \n",
    "\n",
    "3G cellular uses a technology called code division multiple access (CDMA). With CDMA you take a narrowband signal and spread it over a wide bandwidth before transmitting it (using a spread spectrum technique called DSSS). Under frequency selective fading, it’s unlikely that all frequencies will be in a deep null at the same time. At the receiver the spreading is reversed, and this de-spreading process greatly mitigates a deep null.\n",
    "\n",
    "![Alt text](https://pysdr.org/_images/cdma.png)\n",
    "\n",
    "## OFDM \n",
    "\n",
    "4G cellular, WiFi, and many other technologies use a scheme called orthogonal frequency-division multiplexing (OFDM). OFDM uses something called subcarriers, where we split up the signal in the frequency domain into a bunch of narrow signals squashed together. To combat multipath fading we can avoid assigning data to subcarriers that are in a deep fade, although it requires the receiving end to send channel information back to the transmitter quick enough. We can also assign high order modulation schemes to subcarriers with great channel quality to maximize our data rate."
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
